The Estimate of the Basic Reproduction Number for Novel Coronavirus

disease (COVID-19): A Systematic Review and Meta-Analysis

Running title: The Estimate of The Basic Reproduction Number COVID-19

Yousef Alimohamadi1,2

, Maryam Taghdir3 , Mojtaba Sepandi

3,4*

1Pars Advanced and Minimally Invasive Medical Manners Research Center, Pars Hospital,

Iran University of Medical Sciences, Tehran, Iran

2 Department of Epidemiology and Biostatistics, School of Public Health, Tehran University

of Medical Sciences, Tehran, Iran

3 Health Research Center, Lifestyle Institute Baqiyatallah University of Medical Sciences,

Tehran, Iran

4 Department of Epidemiology and Biostatistics, Faculty of Health, Baqiyatallah University

of Medical Sciences, Tehran, Iran

*Correspondence: Mojtaba Sepandi, Health Research Center, Lifestyle Institute, Baqiyatallah

University of Medical Sciences, Tehran, Iran - Department of Epidemiology and Biostatistics,

Faculty of Health, Baqiyatallah University of Medical Sciences, Tehran, Iran - Tel. +98

2187555521 - Fax +98 2188069126 - E-mail: msepandi@gmail.com

Abstract

Objectives: The outbreak of the 2019 novel coronavirus disease (COVID-19) infection is one

of the main public health challenges in the world. Because of high transmissibility, the

COVID-19 causes many morbidities and mortality in the main parts of the world. The true

estimation of the basic reproduction number (R0) can be beneficial in terms of prevention

programs. Because of the present controversy among the original researches about this issue,

the current systematic review and meta-analysis aimed to estimate the pooled R0 for COVID-

19 in the current outbreak.

Methods: International databases, (including Google Scholar, Science Direct, PubMed, and

Scopus) were searched to obtain the studies conducted regarding the reproductive number of

COVID-19. Articles were searched using the following keywords: “COVID-19" and "basic

reproduction number” or "R0". The Heterogeneity of between studies was assessed using the

I2 index, Cochran’s Q test and T

2. The random-effects model was used to estimate the R0 in

this study.

Results: The mean of reported R0 in articles was calculated as 3.38±1.40 with a range of 1.9

to 6.49. According to the results of the random-effects model, the Pooled R0 for COVID-19

was estimated as 3.32(2.81-3.82). According to the results of meta-regression analysis, the

type of used models in estimating R0 does not have a significant effect on heterogeneity

between studies (P: 0.18(

Conclusion: Considering the estimated R0 for COVID-19, reducing the number of contacts

within the population is inevitable to control the epidemic. The estimated overall R0 was

more than WHO estimates.

Keywords: Basic Reproduction Number, COVID-19, Meta-Analysis

INTRODUCTION

In December 2019, a series of pneumonia cases without any identified causes appeared in

Wuhan, Hubei, China, with clinical symptoms similar to viral pneumonia [1-3]. Most of the

mentioned reported cases worked or lived around the local Huanan seafood wholesale market,

where live animals were also sold there [4]. This new human infected virus named by WHO

as the 2019 novel coronavirus (COVID-19) [5]. Because of high contagiousness and

morbidity, this infection considered by WHO as a global urgency [6]. Because of the high

transmissibility of this viral infection, up to 26 Jan 2020 more than 2000 confirmed cases of

COVID-19 were identified in China mainly in Wuhan province [7]. Also as of Feb 15, 2020,

about 66580 cases with 1524 deaths reported from China [8]. The human to human

transmission of this infectious disease was confirmed [9] and this infection reported from

countries other than China [10]. Because of the high infectiousness ability of this virus

among the suspect population, the calculation of basic reproduction number (R0), is essential

in terms of prevention measures [1]. The R0 is an epidemiologic metric that can use to assess

the contagiousness feature of infectious agents. This index presents the average number of

new cases generated by an infected person [11, 12]. The higher amount of R0 refers to more

contagiousness of infectious agents. Since the epidemic began in China, numerous papers

have been published. Because the results of various studies so far have been done in this

regard are somewhat different and controversial, the current systematic review and meta-

analysis aimed to estimate the pooled R0 for the COVID-19 outbreak, using the original

articles published during 2020.

METHODS

Search strategy

This systematic review and meta-analysis performed to estimate pooled R0 of COVID-19 in

articles published in international journals. International databases, (including Google

Scholar, Science Direct, PubMed, and Scopus) were searched to obtain the studies conducted

regarding the reproductive number of COVID-19. Articles were searched using the keywords

“COVID-19" AND "basic reproduction number” OR "R0".

Study selection and data extraction

In the current study, all studies in 2020 which estimated R0 for COVID-19 were entered into

the meta-analysis. The information such as the name of first authors, country, year of study,

model of estimation R0 and estimated R0 value (with 95% confidence interval) were extracted

from the articles.

Statistical analysis

The heterogeneity of between studies was assessed using the I2 index, Cochran’s Q test and

T2. According to I

2 results the heterogeneity can classified into three categories which

include: I2 < 25% (low heterogeneity), I

2 = 25–75% (average heterogeneity), and I

2 index >

75% (high heterogeneity)[13]. Because of the high amount of I2 (99.3%), as well as the

significance of Cochran’s Q (p < 0.0001) the random-effects model was used to estimate of

reproductive number (R0) in this study. Also, the univariate Meta-regression analysis was

used to assess the effect of different models on heterogeneity between studies. The impact of

covariates on the estimated R0 was assessed by univariate meta-regression analysis. In the

current study, just the used Models to estimate R0 by original researches were considered as a

covariate. Data were analyzed by STATA (version 11) software.

Ethics Statement

This paper is a systematic review so it did not need ethical consideration.

RESULTS

We identified 85 studies, of which 23 were duplicates, leaving 62 reports (Figure 1). A total

of 55 reports passed the initial screening, and 23 reports passed full-text assessment for

eligibility. Reasons for exclusion were as follows: reporting of Re and instead of R₀ and

insufficient data. Finally, we included 23 studies in this systematic review (Table 1). No

studies were excluded due to poor quality. In the current study 29 records that estimated R0 of

COVID-19 were entered to analysis. Studies have used different methods to estimate R0 for

COVID-19. All the studies that were included in the Meta-analysis were done in 2020 in

China. The mean of reported R0 in articles was calculated as 3.38±1.40 with a range of 1.9 to

6.49. More information was shown in Table 1.

Pooled estimation of reproductive number (R0)

According to the results of the random-effects model, the pooled R0 for Covid-19 was

estimated as 3.32(2.81-3.82). It means each infected person with COVID-19 can transmit the

infection to on average 4 susceptible people (Figure and Table 2). There was significant

heterogeneity between studies (I2:99.3, P of chi 2 test for heterogeneity :< 0.001 and T

2: 1.72)

(Table 2).

Meta-regression

According to the results of meta-regression analysis, the type of models used for estimation

of R0 doesn’t have a significant effect on heterogeneity between studies (P: 0.81). The

distribution of the estimated R0 according to different models was shown in Figure 3. The

numbers on the x-axis in Figure 3 represent the type of method used in estimating R0. The

coding is as follows: Stochastic Markov Chain Monte Carlo methods=1, Dynamic

Compartmental Model=2, Statistical Exponential Growth Model=3, Statistical Maximum

Likelihood Estimation=4, Mathematical Transmission Model=5, Mathematical Incidence

Decay, and Exponential Adjustment=6, Stochastic Simulations of Early Outbreak

Trajectories=7, Mathematical SEIR-type Epidemiological Model=8, other Mathematical

Models=9, Networked Dynamics Meta Population Model =10, Fudan-CCDC Model=11,

SEIQ Model=12, Coalescent-based Exponential Growth, and a Birth-Death Skyline

Model=13, not mentioned =14.

Figure1. PRISMA Flow Diagram for included studies in current meta-analysis

Records identified through database

searching

(n =80 )

Scre

enin

g

Incl

ud

ed

El

igib

ility

Id

en

tifi

cati

on

Additional records identified

through other sources

(n =5 )

Records after duplicates removed

(n =62 )

Records screened

(n =55 ) Records excluded

(n =25 )

Full-text articles assessed

for eligibility

(n =30 )

Full-text articles excluded,

with reasons

(n = 7 )

Studies included in

qualitative synthesis

(n =23 )

Studies included in

quantitative synthesis

(meta-analysis)

(n =23 )

Table 1. Descriptive characteristics of entered records in the meta-analysis

first author Year Country Model Reproductive

number

LCL UCL

Joseph T Wu et al[14] 2020 China MCMC 2.68 2.47 2.86

Mingwang Shen et al[15] 2020 China Dynamic Compartmental Model 6.49 6.31 6.66

Tao Liu et al(16) 2020 China Statistical Exponential Growth Model 2.90 2.32 3.63

Tao Liu et al[16] 2020 China Statistical Maximum Likelihood

Estimation

2.92 2.28 3.67

Jonathan M. Read et

al[17]

2020 China Mathematical Transmission Model 3.11 2.39 4.13

Maimuna Majumder et

al[18]

2020 China IDEA 2.55 2.00 3.10

WHO[11] 2020 China Mathematical Model 1.95 1.40 2.50

Shi Zhao et al[19] 2020 China Statistical Exponential Growth Model 2.24 1.96 2.55

Shi Zhao et al[19] 2020 China Statistical Exponential Growth Model 3.58 2.89 4.39

Natsuko Imai[20] 2020 China Mathematical Model 2.50 1.50 3.50

Julien Riou and Christian

L. Althaus[21]

2020 China Stochastic Simulations of Early Outbreak

Trajectories

2.20 1.40 3.80

Tang, Biao et al.[22] 2020 China Mathematical SEIR-Type Epidemiological

Model

6.47 5.71 7.23

Qun Li et al[(23] 2020 China Statistical Exponential Growth Model 2.20 1.40 3.90

Sheng Zhang et al[24] 2020 China Statistical Maximum Likelihood

Estimation

2.28 2.06 2.52

Mingwang Shen et al[15] 2020 China Mathematical Model 4.71 4.50 4.92

Zhanwei Du et al[25] 2020 China Statistica Exponential Growth Model 1.90 1.47 2.59

Kamalich Muniz-

Rodriguez et al[26]

2020 China Statistica Exponential Growth Model 3.30 3.10 4.20

Can Zhou[27] 2020 China SEIR Model 2.12 2.04 2.18

Tao Liu[28] 2020 China Statistical Exponential Growth Model 4.50 4.40 4.60

Tao Liu[28] 2020 China Statistical Exponential Growth Model 4.40 4.30 4.60

Ruiyun Li et al[29] 2020 China Networked Dynamic Metapopulation

Model

2.23 1.77 3.00

Sang Woo Park et al[30] 2020 China MCMC 3.10 2.10 5.70

Nian Shao et al[31] 2020 China Fudan-CCDC Mode 3.32 3.25 3.40

Huijuan Zhou et al[32] 2020 China SEIQ Model 5.50 5.30 5.80

Alessia Lai et al[33] 2020 China Coalescent-Based Exponential Growth

And a Birth-Death Skyline Method

2.60 2.10 5.10

Sung-mok Jung et al[9] 2020 China MCMC 2.10 2.00 2.20

Sung-mok Jung et al[9] 2020 China MCMC 3.20 2.70 3.70

Steven Sanche et al[34] 2020 China Statistical Exponential Growth Model 6.30 3.30 11.30

Steven Sanche et al[34] 2020 China Statistical Exponential Growth Model 4.70 2.80 7.60

NOTE: Weights are from random effects analysis

Overall (I-squared = 99.4%, p = 0.000)

Sang Woo Park et al (2020)

Maimuna Majumder et al (2020)

Julien Riou and Christian L. Althaus (2020)

Nian Shao et al (2020)

Can Zhou (2020)

Steven Sanche et al (2020)

Huijuan Zhou et al (2020)

Study

Qun Li et al. (2020)

Ruiyun Li et al (2020)

Sung-mok Jung et al (2020)

Shi Zhao et al (2020)

Tao Liu (2020)

Jonathan M. Read et al (2020)

Zhanwei Du et al (2020)

Joseph T Wu et al (2020)

ID

Steven Sanche et al (2020)

Mingwang Shen et al (2020)

Tao Liu (2020)

Sheng Zhang et al (2020)

Alessia Lai et al (2020)

Shi Zhao et al (2020)

Kamalich Muniz-Rodriguez et al (2020)

Sung-mok Jung et al (2020)

WHO (2020)

Tao Liu et al (2020)

Tang, Biao et al. (2020)

Natsuko Imai (2020)

Mingwang Shen et al (2020)

Tao Liu et al (2020)

3.32 (2.81, 3.82)

3.10 (2.10, 5.70)

2.55 (2.00, 3.10)

2.20 (1.40, 3.80)

3.32 (3.25, 3.40)

2.12 (2.04, 2.18)

4.70 (2.80, 7.60)

5.50 (5.30, 5.80)

2.20 (1.40, 3.90)

2.23 (1.77, 3.00)

2.10 (2.00, 2.20)

3.58 (2.89, 4.39)

4.40 (4.30, 4.60)

3.11 (2.39, 4.13)

1.90 (1.47, 2.59)

2.68 (2.47, 2.86)

ES (95% CI)

6.30 (3.30, 11.30)

4.71 (4.50, 4.92)

4.50 (4.40, 4.60)

2.28 (2.06, 2.52)

2.60 (2.10, 5.10)

2.24 (1.96, 2.55)

3.30 (3.10, 4.20)

3.20 (2.70, 3.70)

1.95 (1.40, 2.50)

2.92 (2.28, 3.67)

6.47 (5.71, 7.23)

2.60 (1.50, 3.50)

6.49 (6.31, 6.66)

2.90 (2.32, 3.63)

100.00

2.58

3.67

3.16

3.84

3.84

2.06

3.80

%

3.11

3.63

3.83

3.54

3.83

3.45

3.67

3.82

Weight

1.13

3.81

3.83

3.81

2.87

3.79

3.67

3.70

3.67

3.58

3.53

3.34

3.82

3.61

3.32 (2.81, 3.82)

3.10 (2.10, 5.70)

2.55 (2.00, 3.10)

2.20 (1.40, 3.80)

3.32 (3.25, 3.40)

2.12 (2.04, 2.18)

4.70 (2.80, 7.60)

5.50 (5.30, 5.80)

2.20 (1.40, 3.90)

2.23 (1.77, 3.00)

2.10 (2.00, 2.20)

3.58 (2.89, 4.39)

4.40 (4.30, 4.60)

3.11 (2.39, 4.13)

1.90 (1.47, 2.59)

2.68 (2.47, 2.86)

ES (95% CI)

6.30 (3.30, 11.30)

4.71 (4.50, 4.92)

4.50 (4.40, 4.60)

2.28 (2.06, 2.52)

2.60 (2.10, 5.10)

2.24 (1.96, 2.55)

3.30 (3.10, 4.20)

3.20 (2.70, 3.70)

1.95 (1.40, 2.50)

2.92 (2.28, 3.67)

6.47 (5.71, 7.23)

2.60 (1.50, 3.50)

6.49 (6.31, 6.66)

2.90 (2.32, 3.63)

100.00

2.58

3.67

3.16

3.84

3.84

2.06

3.80

%

3.11

3.63

3.83

3.54

3.83

3.45

3.67

3.82

Weight

1.13

3.81

3.83

3.81

2.87

3.79

3.67

3.70

3.67

3.58

3.53

3.34

3.82

3.61

0-11.3 0 11.3

Figure2. Forest plot of the pooled basic reproductive number (R0) for COVID-19

Table2. Pooled Estimation of reproductive number (R0) for COVID-19

Pooled Estimate(95%

CI)

Q I2 T

2

3.32(2.81-3.82)

23

45

67

Re

pro

du

ctive n

um

be

r

0 5 10 15Model

Figure3. The distribution of estimated R0 according to different models.

DISCUSSION

It is necessary to estimate the amount of R0 to determine the severity and size of the epidemic,

as well as to design appropriate interventions and responses to protect the population against

disease and to control of the epidemic [35]. The estimated R0 value is important in infectious

disease epidemiology because the force of infection could be reduced by 1 − 1 /R0 to

eliminate the disease outbreak. For example, at R0 = 2.5 this fraction is 60%, but at R0 = 3.2

this fraction is 68.7%. Mathematical models play an important role in decision making during

outbreak control [36]. Our systematic review and meta-Analysis found the overall R0 to be

3.32(2.81-3.82), which is more than WHO estimates of 1.4 to 2.5(11) but similar to results of

a former review with 12 articles that have had been conducted in China (11). Our estimation

is similar in comparison with the R0 values of the SARS epidemics (R0 = 4.91) in Beijing,

China [37], and MERS in Jeddah (R0 = 3.5–6.7), Saudi Arabia [38]. Such a high R0 indicates

that the virus can go through at least three–four generations of transmission [22]. Similar to

reviews of R0 for other pathogens [39-41] our result highlight that R0 is not an intrinsic value

characteristic of a given pathogen, but rather describes the transmissibility of that pathogen

within the specific population and setting under study. The estimated R0 depends on some

issues such as the social and demographical variables, estimation method used, and the

validity of the underlying assumptions and the biology of the infectious agent. For example,

the frequency of contacts may depend on population size and cultural issues. These factors

can vary across regions. In addition, estimates of R0 may be somewhat error-prone due to

some reasons such as data insufficiency and short onset time period. The more studies are

done and the more data is produced, the hope is that this error will be reduced. Our results

showed that there was significant heterogeneity between studies (I2:99.3, P of chi

2 test for

heterogeneity :< 0.001 and T2: 1.72). One reason for this issue is that it is hard to calculate

the exact number of infected cases during an outbreak. The variability in R0 values reported

by different studies indicates that precisely estimating of R0 is rather difficult. Also, the R0

can be affected by environmental factors and modeling methodology [12]. There are lots of

calculation methods for R0 [42]. Our review was restricted to Chinese articles. For other

countries surveillance data is needed to either calculate R0 value or R0 estimates extrapolate

from a comparable setting.

Consideration of the reasons for reporting high levels of R0 in some studies also seems

necessary. Modeling assumptions may be one reason for this issue. Usually, high R0 values

are calculated in the early stages of the epidemic, because of the small sample size as well as

the lack of awareness about the disease and inadequate preventive measures. Since the

number and patterns of people’s contacts in different populations vary because of some

reasons, such as the general culture and the level of literacy in the community, the value of R0

varies among different populations, or even among subgroups of a single population. In fact,

the total value of R0 in a population is the average of the R0 subtypes of that community. It is

therefore important to note that even if the total R0 value in a population is low (even less

than 1), the likelihood of transmission in some subgroups of that population may still be high.

Given the rapid spread of the disease, the dependency of the effectiveness of control

measures to some factors such as the frequency of asymptomatic infections and the potential

for disease transmission before symptoms onset, COVID-19 seems to be relatively difficult to

control. R0 is dependent on the population as well as the method of calculation and quantifies

the transmissibility of a disease in a population. Our findings suggest that measures such as

preventing human population gatherings, restricting the transportation system, closing

schools, and universities, etc., may be necessary to control the epidemic.

SUPPLEMENTAL MATERIALS

None

CONFLICT OF INTEREST

The authors have no conflicts of interest associated with the material presented in this paper.

FUNDING

There was no external funding required for this project.

ACKNOWLEDGEMENTS

We thank all authors involved in collecting and processing data.

AUTHOR CONTRIBUTIONS

YA, M S conceived the study design, Search of articles, provided data, led the analysis,

prepare drafts of the manuscript, M T data extraction, prepare drafts of the manuscript and

final edition. All authors approved final version of manuscript.

ORCID

Yousef Alimohamadi https://orcid.org/0000-0002-4480-9827

Maryam Taghdir https://orcid.org/0000-0003-2853-0196

Mojtaba Sepandi https://orcid.org/0000-0001-6441-5887

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